Techniques have been proposed for estimating and correcting phase errors from digital holography (DH) data using image sharpening algorithms. Such algorithms are designed for cases where multiple independent data sets are available, and the techniques are known as multi-shot DH. For cases where only a single data set is available, known as single-shot DH, image sharpening algorithms perform poorly, especially in the presence of strong turbulence.
Digital Holography (DH) uses coherent illumination and heterodyne detection to sense the amplitude and phase of light scattered off an object's surface. The resulting data is sensitive to phase errors caused by index-of-refraction perturbations in the atmosphere, other propagating medium, or optical systems. These errors can be estimated directly from the DH data for the purposes of forming focused images or for wave-front sensing. Image sharpening (IS) techniques estimate phase errors from DH data by maximizing an image sharpness metric. The images are formed from estimates of the complex-valued reflection coefficient, g, given by the complex-valued ratio of the reflected field to the incident field. For surfaces which are rough relative to the illumination wavelength, this leads to images with short scale (high-spatial frequency) spatial variations known as speckle. Image sharpening algorithms require incoherent averaging of multiple speckle realizations, referred to as multi-shot DH, to accurately estimate phase errors. As such they are not applicable when only a single data realization (single shot) is available. This may be the case, for example, when an object to be imaged is in motion.